\newproblem{lay:6_2_26}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 6.2.26}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Suppose $W$ is a subspace of $\mathbb{R}^n$ spanned by $n$ non-zero orthogonal vectors. Explain $W=\mathbb{R}^n$.
}{
   % Solution
	A set of orthogonal vectors is always linearly independent (see Theorem 6.2.4). We also know that any set of $n$ linearly independent vectors is a basis of $\mathbb{R}^n$ (see
	Theorem 4.5.12). So, the same set spans $W$ and $\mathbb{R}^n$, so both sets are equal.
}
\useproblem{lay:6_2_26}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
